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Minimum-energy broadcasting in multi-hop wireless networks using a single broadcast tree

Minimum-energy broadcasting in multi-hop wireless networks using a single broadcast tree. Authors: Ioannis Papadimitriou and Leomidas Georgiadis Publisher: Mobile Networks and Applications 11, 361–375, 2006 Present: Min-Yuan Tsai ( 蔡旻原 ) Date: October, 16, 2007.

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Minimum-energy broadcasting in multi-hop wireless networks using a single broadcast tree

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  1. Minimum-energy broadcasting in multi-hop wireless networks using a single broadcast tree Authors:Ioannis Papadimitriou and Leomidas Georgiadis Publisher:Mobile Networks and Applications 11, 361–375, 2006 Present:Min-Yuan Tsai (蔡旻原) Date:October, 16, 2007 Department of Computer Science and Information Engineering National Cheng Kung University, Taiwan R.O.C.

  2. Outline • 1. Introduction • 2. Definitions and problem description • 3. Broadcasting using a single broadcast tree • 4. Numerical results • 5. Conclusion

  3. Introduction • In this paper, the authors focus on the problem of energy-efficient broadcasting in wireless networks where omni-directional antennas are used and there is flexibility of power adjustment. • Common solution depends on the source nodethat initiates the broadcast request. (Every time a node needs to broadcast some information to all other nodes in the network, the algorithm for the broadcast tree construction is executed for the specific source node.) • Each node in the network has to keep track of n broadcast trees, one for each of the possible source nodes (n is the number of nodes in the network). • large memory space

  4. Introduction (cont.) • The authors proposed minimum-energy broadcasting using a single broadcast tree(SBT) to simplified the above situation . • Advantages of the proposed scheme • Generalnetworks • Independenceof the source node – considerable simplification, scaling • Approximation ratio close to bestachievable bound in polynomial time

  5. Outline • 1. Introduction • 2. Definitions and problem description • 3. Broadcasting using a single broadcast tree • 4. Numerical results • 5. Conclusion

  6. Model for Wireless Broadcasting • Definition: • G(N , L): connected undirected graph • cl> 0: power needed for successful transmission over link l=(i , j) • If node i transmits with power p, it can reach any node j for which c (i , j) ≤ p • Ts=(N , LTs): s-rooted directed spanning tree that induced by undirected tree T • node s transmits with power

  7. Model for Wireless Broadcasting(cont.) • Example: • T : {(A,B) , (A,C) , (B,D)} (undirected) • TA and TD (directed) are induced by T • , C & D are leaves node in TA • , (D,B) is outgoing link of D in TD

  8. The Minimum-Energy Broadcast Problem • : total power consumed for broadcasting from source node s • In general, for different source nodes, the trees that minimize the sum of node powers are different (each node has to keep track of |N| broadcast trees, one for every possible source) • To simplify the above situation we have to “Find a single (undirected) spanning tree T to be used by all nodes for broadcasting, such that the sum of consumed node powers P(Ts) is minimized for any source node s”. • Each node needs to store only a small set of links that belong to tree T • Processing of broadcast information is minimal(scaling to larger networks)

  9. The Minimum-Energy Broadcast Problem (cont.) • Two open issues: If all broadcasts take place on the same tree, then • Issue 1 : Certain broadcasts may need much more total power than others, depending on the source node (widely varying total power consumption for different source nodes). • Issue 2 : If one attempts to find a tree for which the total powers consumed for broadcasting initiated by different source nodes are approximately the same, then, for a given source node, the resulting total power may be far away from the optimal.

  10. Outline • 1. Introduction • 2. Definitions and problem description • 3. Broadcasting using a single broadcast tree • 4. Numerical results • 5. Conclusion

  11. Broadcasting using a single broadcast tree • Addressing Issue 1 : We use the following Corollary. • If the same spanning tree T is used for broadcasting by all nodes, then the total broadcast power consumption for source node s is at most twice the total broadcast power consumption for any other source node s΄, P(Ts)≤ 2P(Ts΄). • Addressing Issue 2 : We propose a polynomial time approximation algorithm for the construction of a single broadcast tree . • For any source node s, the total power consumed for broadcasting using tree has an approximation ratio 2H(n-1) with respect to the optimal power. • Approximation ratio close to the bestachievable bound in polynomial time (n=|N| is the number of nodes in the network and H(n) is the harmonic function)

  12. Broadcasting using a single broadcast tree (cont.) • Single Broadcast Tree (SBT) algorithm: • At each iteration, SBT maintains a forest of trees in the network, such that each node belongs to a forest tree. • Initially, each node constitutesa forest tree. • The forest is expanded by joining trees through nodes, so that the “incremental power consumed per joined tree” is minimal. • This is achieved by examining the adjacent links of every node i in the network that terminate outside the tree to which node i belongs. • The algorithm terminates when the forest consists of a single (undirected) spanning tree.

  13. Broadcasting using a single broadcast tree (cont.) • Example of SBT algorithm : • Node imin is selected to be joined with the forest tress TF1 and TF2. • Link lmin joins tree TFmin with TF1 . • Only one of the links (imin , m) , (imin , n) must be selected to join tree TFmin with TF2 to avoid the creation of cycle.

  14. Broadcasting using a single broadcast tree (cont.) • A minimum spanning tree (MST) of G is a spanning tree whose sum of link costs is minimal. • For any source node s, the total power consumed for broadcasting using a minimum spanning tree, is at most Δ times the optimal power, where Δ is the maximum node degree in the network. • For any source node s, the total power consumed for broadcasting using a single broadcast tree has an approximation ratio 2H(n-1) with respect to the optimal power where H(n) is the harmonic function. • MST may be a good candidate for broadcasting in sparse networks.

  15. Outline • 1. Introduction • 2. Definitions and problem description • 3. Broadcasting using a single broadcast tree • 4. Numerical results • 5. Conclusion

  16. Numerical results • Algorithms compared: • 1) Broadcast Incremental Power algorithm (“BIP”) • 2) Single Broadcast Tree (“SBT”) • 3) Minimum Spanning Tree (“MST”) • Networks: • 1) With a specified number of nodes (20,40,…,100) in a rectangular grid of 100×100 points (The power needed for successful transmission over link (i, j ) depends on the distance d(i,j) between the two nodes and it is given by c(i,j) = da(i,j ), where a is the propagation loss exponent.) • 2) “Special” nodes added to the grid – 3-dimensional network • Performance metric: Average total broadcast power consumption

  17. Numerical results (cont.) a = 2 , complete networks a = 4 , complete networks • BIP determines a different broadcast tree for every possible source node, while SBT algorithm constructs a single tree used by all nodes for broadcasting. • Average tree power of SBT is slightly larger than that of BIP. • The difference in performance of the algorithms vanishes for larger values of a. The “penalty” of using longer links increases and all algorithms converge to MST.

  18. Numerical results (cont.) • The power of a link between the “special” node and any other node on the grid at distance d is f  d2, where f is a factor 0 < f ≤ 1. • There is a range of values of f for which SBT outperformssignificantly BIP. • SBT succeeds in selecting links of “special” node when they are more cost efficient. a = 2, 1 “special” node added to the sparse networks, factor f = 0.1 Ratio of avg. tree power of SBT to BIP, a = 2, 100-node sparse networks + 1 “special” node

  19. Numerical results • SBT algorithm performs fairly well, compared to BIP algorithm, for networks represented by unit disk graphs, while using a single broadcast tree. • There are interesting instances of general networks, for which SBT algorithm significantly outperforms BIP and MST. • MST algorithm performs worse for most of the network instances considered. • SBT algorithm presents a good compromise between simplicity and achieved performance.

  20. Outline • 1. Introduction • 2. Definitions and problem description • 3. Broadcasting using a single broadcast tree • 4. Numerical results • 5. Conclusion

  21. Conclusion • The main contribution of this paper is that we do not have to determine a different broadcast tree every time a source node initiates a broadcast request. • Some further study: • Network environments with high mobility and frequent topological changes. • Energy-limited and resource-limited environment, Lifetime maximization. • Dynamicpower assignments

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